If you just replace coal with natural gas in the same plant to heat the water it is not significantly less CO2
Burning coal is pretty much just turning bulk carbon into carbon dioxide. Burning natural gas (methane, CH4) creates carbon dioxide, too, of course, but also releases energy from burning the hydrogen to make water. As a result, the combustion of natural gas produces less CO2 for the same energy output. From the Energy Information Agency - Pounds of CO2 emitted per million BTU of energy: Coal (anthracite): 228.6 Gasoline: 157.2 Natural Gas: 117.0 [I'll apologize for the units - I'm just quoting the result. If you must know, 1 lb / 1e6 BTU is equivalent to 0.43e-3 kg/MJ. Or, just look at the number as a figure of merit: lower is better.] more data here
It is even more effective than that- these numbers don't take plant efficiency into consideration. The "per million BTU of energy" is just the amount of heat produced, not the amount of electricity. A very efficient traditional coal plant is about 35-40% efficient in turning the heat into electrical power. A typical combined cycle gas power plant is about 57-60% efficient due to the nature of the different cycle. So, on a per-MW produced basis, Natural gas looks a lot better.
It also doesn't hurt that natural gas is at all-time low prices in the US thanks to our gas boom and the high cost of transporting natural gas across oceans. Gas is cheaper than coal now in many places. The only coal plants which are going to survive are the more efficient plants with short coal supply lines. It has little to do with environmental concerns, it is strictly an economic calculation in many cases. The environmentalists didn't defeat coal, the accountants did.